Daca A'(1,-1), B'(3,1) si O(0,0) sunt mijloacele laturilor BC, AC si AB ale unui triunghi ABC, determinati coordonatele punctelor A,B,C. 

De 2 zile ma tot gandesc si nu-i dau de capat, va rog frumos un raspuns. Multumesc anticipat.



Răspuns :

[tex]O(0,0)=O( \frac{x_A+x_B}{2}, \frac{y_A+y_B}{2})=>x_A+x_B=0;y_A+y_B=0[1]\\ A'(1,-1)=A'( \frac{x_B+x_C}{2},\frac{ y_B+y_C}{2})=>x_B+x_C=2;y_B+y_C=-2[2]\\ B'(3,1)=B'( \frac{x_A+x_C}{2}, \frac{y_A+y_C}{2})=>x_A+x_C=2;y_A+y_C=2\\ Din[1]-[2]=>x_A-x_C=-2;x_A+x_C=4=>\\ x_A;x_C=4;x_B=-2\\ Din[1]-[2]=>y_A-y_C=2;y_A+y_C=2=>\\ y_A=2;y_C=0;y_B=-2\\ A(2;2);B(-2,-2);C(4;0).[/tex]